Local Quantum Gravity

TL;DR

This paper explores the ultraviolet behavior of quantum gravity using a functional renormalisation group approach, incorporating full propagators and the graviton three-point function, confirming the asymptotic safety scenario.

Contribution

It introduces the dynamical graviton three-point function into the functional renormalisation group analysis of quantum gravity, enhancing the system's self-consistency.

Findings

Confirmation of the asymptotic safety scenario with a non-trivial UV fixed point.

Demonstration of the importance of momentum locality for the consistency of the flow.

Link between momentum locality of graviton functions and diffeomorphism invariance.

Abstract

We investigate the ultraviolet behaviour of quantum gravity within a functional renormalisation group approach. The present setup includes the full ghost and graviton propagators and, for the first time, the dynamical graviton three-point function. The latter gives access to the coupling of dynamical gravitons and makes the system minimally self-consistent. The resulting phase diagram confirms the asymptotic safety scenario in quantum gravity with a non-trivial UV fixed point. A well-defined Wilsonian block spinning requires locality of the flow in momentum space. This property is discussed in the context of functional renormalisation group flows. We show that momentum locality of graviton correlation functions is non-trivially linked to diffeomorphism invariance, and is realised in the present setup.